TAMPA, Fla. — The Islanders’ problem of late has been scoring goals, not preventing them. Now they found a new problem.

On Friday night, the Isles dropped a 7-4 game to the Lightning, which pumped 42 shots on goal and drove toward Thomas Greiss early and often. The result: The Islanders allowed their highest goal total in a game this season.

After the Isles battled back twice to tie it at 3-3 and 4-4, Tyler Johnson tapped in a rebound with 9:51 left in the third period. Greiss stopped Jonathan Marchessault’s initial shot, but Johnson had an easy rebound as Josh Bailey fell while trying to play the puck.

Jason Garrison scored only 23 seconds later and Victor Hedman hit the empty net with 1:25 to play.

“They have a good offensive team,’’ Greiss said. “I think we’re not getting many bounces, either. If the puck hit the post and bounced away other nights, it bounced right to them tonight.”

Said Travis Hamonic, “As a group, we haven’t been playing our best of late, but I think it’s been because we haven’t been scoring enough. Tonight we didn’t defend well all over the ice.”

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The Isles got to the third period tied at 3-3, but Andrej Sustr’s point shot beat Greiss at 6:03. Before the crowd had quieted down, Nikolay Kulemin tied it at 6:22 with his first goal in 22 games.

The Isles, who headed to Raleigh for a quick turnaround Saturday night, remained two points ahead of the Flyers in the Metropolitan Division and one point behind the Penguins in the tight playoff chase.

The Islanders put together a poor final minute of the second period, but Greiss kept it tied with three saves in the final 30 seconds of the period. He had 27 through two periods, 16 in the second.

The Isles clawed back from a two-goal deficit in that middle period despite having loads of trouble with the Lightning’s speed. Steven Stamkos buried a rebound into a wide-open net to put Tampa Bay up 3-1 at 5:02 of the second, but Shane Prince answered 23 seconds later. He stole the puck at the Islanders’ line, skated in two-on-one with Anders Lee and snapped a pretty shot over Ben Bishop’s shoulder with the home crowd still cheering Stamkos’ goal.

The Islanders pulled even on Johnny Boychuk’s long shot at 16:18 that took a few hops on its way in. John Tavares curled and dropped the puck to the point, where it hopped toward Boychuk. He fungoed it toward the net, where Sustr tipped it past his own goaltender.

“It was good to see us answer a couple times,” coach Jack Capuano said. “But we still have some guys who need to do a better job away from the puck. That hurt us.”

The Islanders played a good road period in the first but let too many chances slip. They had three power plays in the opening period, two in the first nine minutes, but converted only after the second advantage expired.

Ryan Strome hit Brock Nelson in the right faceoff circle and he snapped off a shot just as Garrison got to him. Bishop never saw the rising wrister, Nelson’s 25th, at 8:54.

Lee, who had a goal waved off on that second advantage when his backhand try went through Bishop’s legs after referee Gord Dwyer already had blown his whistle, figured in an ugly scene soon after.

He was battling for position with Anton Stralman in front of Bishop and won the battle. Stralman’s right skate caught in the ice as he fell, twisting his leg awkwardly. He had to be helped off the ice, and his night — and possibly his season — was over.

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The Lightning announced that Stralman suffered a non-displaced fracture of his right fibula on the play.

“That’s the last thing I want to see,” Lee said. “We were battling in front and the next thing I know, he’s down. You hate to see that. I feel bad, but it was just a battle.”